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Falasconi, M., Gutierrez, A., Pardo, M., Sberveglieri, G., Marco, S., (2010). A stability based validity method for fuzzy clustering Pattern Recognition , 43, (4), 1292-1305

An important goal in cluster analysis is the internal validation of results using an objective criterion. Of particular relevance in this respect is the estimation of the optimum number of clusters capturing the intrinsic structure of your data. This paper proposes a method to determine this optimum number based on the evaluation of fuzzy partition stability under bootstrap resampling. The method is first characterized on synthetic data with respect to hyper-parameters, like the fuzzifier, and spatial clustering parameters, such as feature space dimensionality, clusters degree of overlap, and number of clusters. The method is then validated on experimental datasets. Furthermore, the performance of the proposed method is compared to that obtained using a number of traditional fuzzy validity rules based on the cluster compactness-to-separation criteria. The proposed method provides accurate and reliable results, and offers better generalization capabilities than the classical approaches.

Keywords: Fuzzy c-means, Cluster validity, Number of clusters, Cluster stability